From the information given in the statement, you can see that the original function, before the transformation, is
[tex]g(x)=x^2[/tex]
Now, by the rules of transformation of functions you know that:
*g(x - h) moves the function g(x) h units right
*g(x) + k moves the function g(x) k units up
So, in this case, you have
[tex]\begin{gathered} f(x)=(x-3)^2+5 \\ h=3 \\ k=5 \end{gathered}[/tex]
Which implies that the original graph will move 3 units to the right and 5 units up.
Therefore, the graph that represents the given quadratic function is the graph of option B.
